Effects of payoff-related velocity in the co-evolutionary snowdrift game

Previous studies concerning mobile populations seldom distinguish mobility on the individual level. In these models, all individuals have the identical moving speed and this moving speed has not been clearly defined in terms of its relevance to other features intrinsic to individual. Here we investigate the evolution of cooperation with a minimal co-evolutionary snowdrift game in which the payoff-dependent velocity as well as velocity diversity is taken into account. We find that the fate of evolution in such scenarios is precisely ruled both by population mobility and the inherent parameter of the snowdrift game. The outside-in and inside-out like attacks on cooperator clusters (C-clusters) are triggered in the Monte Carlo simulation. The results show that low mobility can lead to a plateau of full cooperation provided the challenge to cooperate is not too high, and also that high mobility always inhibits cooperation. Nevertheless, the phase transition diagram implies moderate population mobility most benefits the survival of cooperators when cooperation faces the greater challenge. Finally, the evolution of strategies seemingly rises superior to selection strength once the mobility intensity is fixed. Our findings may shed new light on the evolution of strategies in mobile systems.